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A Convolution Theorem Related to Quaternion Linear Canonical Transform

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  • Mawardi Bahri
  • Ryuichi Ashino

Abstract

We introduce the two‐dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in quaternion algebra setting. Based on the definition of quaternion convolution in the QLCT domain we derive the convolution theorem associated with the QLCT and obtain a few consequences.

Suggested Citation

  • Mawardi Bahri & Ryuichi Ashino, 2019. "A Convolution Theorem Related to Quaternion Linear Canonical Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnlaaa:v:2019:y:2019:i:1:n:3749387
    DOI: 10.1155/2019/3749387
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    References listed on IDEAS

    as
    1. Mawardi Bahri, 2014. "On Two-Dimensional Quaternion Wigner-Ville Distribution," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-13, January.
    2. Mawardi Bahri & Resnawati & Selvy Musdalifah, 2018. "A Version of Uncertainty Principle for Quaternion Linear Canonical Transform," Abstract and Applied Analysis, Hindawi, vol. 2018, pages 1-7, May.
    3. Kit Ian Kou & Jian-Yu Ou & Joao Morais, 2013. "On Uncertainty Principle for Quaternionic Linear Canonical Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, April.
    4. Kit Ian Kou & Jian-Yu Ou & Joao Morais, 2013. "On Uncertainty Principle for Quaternionic Linear Canonical Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Mawardi Bahri, 2014. "On Two‐Dimensional Quaternion Wigner‐Ville Distribution," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    6. Mawardi Bahri & Ryuichi Ashino & Rémi Vaillancourt, 2013. "Convolution Theorems for Quaternion Fourier Transform: Properties and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Mawardi Bahri & Ryuichi Ashino & Rémi Vaillancourt, 2013. "Convolution Theorems for Quaternion Fourier Transform: Properties and Applications," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    8. Mawardi Bahri & Ryuichi Ashino, 2016. "A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-11, January.
    9. Mawardi Bahri & Resnawati & Selvy Musdalifah, 2018. "A Version of Uncertainty Principle for Quaternion Linear Canonical Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2018(1).
    10. Mawardi Bahri & Ryuichi Ashino, 2016. "A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
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